Date: Mar 21, 2013 6:36 AM
Author: William Hughes
Subject: Re: Matheology § 224
On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:

<snip>

> > There is such a thing as a sufficient set of

> > lines (all sufficient sets are composed

> > entirely of unnecessary lines, which means

> > that you can remove any finite set of lines

>

> Why only finite sets?

You can only use induction to prove

stuff about finite sets.

> What property is changed if infinitely many are

> there? If there are infinitely many unnecessary lines, they all can be

> removed - by their property of being unnecessary.

Nope, their property of being unnecessary means

that *any one* line can be removed.

Once we remove one line, we are left with

a new set of unnecessary lines. We can

remove one of these lines.

From induction we get that

any finite set of lines can

be removed.